Factors
Factors are whole numbers that divide evenly into a given number, with no remainder, in Grade 6 math (Saxon Math, Course 1). To find all factors of a number, test divisibility starting from 1 and work upward in pairs: 1 pairs with the number itself, 2 pairs with half the number if even, and so on. For example, factors of 24: 1×24, 2×12, 3×8, 4×6 → factors are {1, 2, 3, 4, 6, 8, 12, 24}. Every number has at least two factors (1 and itself); primes have exactly two. Knowing factors is essential for simplifying fractions (finding GCF), finding LCM, and algebraic factoring.
Key Concepts
Contextual Explanation Factors are the building blocks you multiply to get another number, like ingredients in a recipe! If you can divide a number by another with zero leftovers, you've found a factor. This trick helps break down big numbers into simple parts, making them much easier to work with. Full Example Problem : What are the factors of 14? Solution : The factors of 14 are all numbers that divide 14 with no remainder. We can find them by testing division or finding multiplication pairs. $14 \div 1 = 14$ $14 \div 2 = 7$ $14 \div 7 = 2$ $14 \div 14 = 1$ These divisions show the factors are 1, 2, 7, and 14 . This can also be shown with a 1 by 14 rectangle and a 2 by 7 rectangle.
Common Questions
What is a factor?
A factor of a number divides into it evenly (no remainder). For example, 3 is a factor of 12 because 12 ÷ 3 = 4.
How do you list all factors of 24?
Test factor pairs: 1×24, 2×12, 3×8, 4×6. All factors: {1, 2, 3, 4, 6, 8, 12, 24}.
How many factors does a prime number have?
Exactly two: 1 and the number itself. For example, 7's only factors are 1 and 7.
What is the greatest common factor (GCF) of two numbers?
The largest factor they both share. GCF(12, 18) = 6 because 6 is the largest number in both factor lists.
How are factors used in simplifying fractions?
Find the GCF of numerator and denominator, then divide both by it. For 12/18, GCF = 6, so 12/18 = 2/3.